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2008/12/25 RCNP. G 行列理論に基づくバリオン - 核間相互作用の導出. 都留文科大学    山本 . 共同研究者 古本 櫻木 (大阪市大). G-matrix interaction を使うことの意味 核力に基づく理解      核模型における有効相互作用. 核内での核力の特徴が G-matrix を通して現れる. たとえば、 nuclear saturation property density-dependent effective interaction central/LS/tensor components.

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slide1

2008/12/25 RCNP

G行列理論に基づくバリオン-核間相互作用の導出

都留文科大学

   山本 

共同研究者 古本 櫻木 (大阪市大)

slide2

G-matrix interactionを使うことの意味

核力に基づく理解

     核模型における有効相互作用

核内での核力の特徴がG-matrixを通して現れる

たとえば、

nuclear saturation property

density-dependent effective interaction

central/LS/tensor components

slide3

T = V+VPT = V+VPV+VPVPV+ ・・・

Ladder sum

Pに多体効果を入れるとTがGになる

媒質中での2体散乱

slide5

Nuclear saturation given by various NN potentials

(G-matrix calculations)

Gap choice

E/Aで4~5 MeVの差

これは大きい

Continuous choice

Repulsive three-body effect in high-density region

is necessary for nuclear saturation

slide6

Baldo et al. arXiv:astro-ph/0312446

4ρ0

LOBT(C.C.) は高密度まで信頼できる !!!

slide7

G行列理論に基づくnuclear saturation

LOBT with continuous choice is reliable

up to high density

Role of Three-Body Interaction

(TBA+TBR) is essential for

saturation problem

slide8

For nuclear saturation,

role of TBF is indispensable !

Typically

Fujita-Miyazawa

diagram

●Attraction at low densities

●Repulsion at high densities

Phenomenological TBR by Illinois group

for instance

slide9

TBA

Derivation of effective two-body potential from TBF

by Kasahara, Akaishi and Tanaka

Fujita-Miyazawa diagram

slide10

TBRは実在する!

Saturation curve (incompressibility)に不可欠

中性子星の最大質量

・・・

その起源は?

Pure phenomenological

Meson exchange diagrams

Relativistic (Z-diagram)

 ・・・

slide11

Phenomenological modeling of

Three-Body Repulsion in ESC04

Necessary for maximum mass

of neutron star

Universal among

NNN, NNY, NYY…

Three-body force due to triple-meson correlation

Reduction of meson mass in medium

MV(ρ)=MV exp(-αρ) for vector mesons

Medium-Induced Repulsion

slide12

TBA

Baldo

TBR

Similar curve is obtained

slide13

Maximum-mass problem of neutron stars

Importance of universal TBR

slide14

G は ωと kF(Qを通じて) に依存する

モデル化して有限系に適用

(nuclear-matter G-matrix + LDA)

例えば

Density-Dependent interaction

(ω-depをkF-depに吸収する)

散乱問題への応用では G(r; kF, Ein)

slide15

OMP derived from G-matrix interaction

incident energy

ω

ω-rearrangement

Imaginary part

slide16

CEG83

Old calculation by Kasahara-Akaishi-Tanaka

slide17

From CEG83 to CEG07

Modern NN interaction model ESC

Continuous choice for intermediate spectra

Including TBA (Fujita-Miyazawa) + TBR

Up to higher partial waves

on the basis of saturation mechanism

slide18

16O + 16O elastic scattering E/A = 70 MeV

Effect of three-body force

T.Furumoto, Y. Sakuragi and Y. Yamamoto, (Submitted to Phys.Rev.C rapid communication)

slide19

同じ処方箋で

hyperon-nucleus potentialを攻めてみよう

slide20

Nijmegen soft-core models

(NSC89/97, ESC04/07)

Origin of cores

pomeron

ω meson

Repulsive cores are similar

to each other in all channels

Different from

Quark-model core

Tamagaki’s Quark Pauli-forbidden states ?

ハイパー核で領域Ⅲを見れるか?

原子核現象を通じて核力の領域IIIの異なる

modelingを区別することはできなかった

slide21

ESC04 modeling

PS, S, V, AV nonets

not taken

(ππ),(πρ),(πω),(πη),(σσ)

+(πK),(πK*)・・・ strangeness exchange

ESC07

PS-PS exchange

small spin-orbit interaction

Quark-model-like core

slide22

∑-Nucleus potentials U∑

Intermediate states in (π,K) reactions

∑-nucleus scattering

・・・・・

Interesting problems

repulsive ?

isospin-dependence

spin-orbit interaction

imaginary parts (scattering & conversion)

slide23

Are repulsive ∑-potentials obtained from Nijmegen models?

NHC-F ok

but…

No(maybe)standard NSC/ESC modeling

in spite of elaborate works by Rijken

Import the feature of quark model !

slide24

various

Nijmegen

Models

21S023S141S043S1 sum

Fss 6.1 -20.2 -8.8 48.2 +9.8

fss2 6.7 -23.9 -9.2 41.2 +7.5

QM-based

models

slide25

Feature of QM core

K. Shimizu, S. Takeuchi and A.J. Buchmann, PTP, Suppl. 137(2000)

Almost Pauli-forbidden states

slide26

Adjust V[51

Pauli-forbidden state exist in V[51]

slide27

Recent Nijmegen approach

ESC core = pomeron + ω

Assuming

“equal parts” of ESC and QM are similar to each other

Almost Pauli-forbidden states in [51] are taken

into account by changing the pomeron strengths

for the corresponding channels

gPsqrt(2.5) gP

ESC07 models

slide29

Optical potential

∑-nucleus folding potential

derived from complex G-matrix

G∑N(r; E, kF)

In N-nucleus scattering problem

physical observables can be reproduced

with “no free parameter”

slide31

relation

Effective Mass and E-dependence of U∑

with ESC07

If m∑* > 1 then U’∑ < 0

slide34

ESC07

Pauli-forbidden

states

U∑(real) cancelingが効く

W∑には”2乗和”で効く

Wscattが大きい理由

slide35

Improved LDA by JLM

Phys. Rev. C10 (1974) 1391

simple LDA : U(ρ(r),E)

slide37

NW*Uimag

NW=0.65

Same as NA case

In general, G-matrix overestimates Uimag as seen in N-nucleus systems

slide38

Summary

G-matrix method (nuclear matter approach)

is very powerful to describe N-nucleus and

Nucleus-nucleus scattering observables

starting from realistic NN interaction models

On the same ground ∑-nucleus potentials are

derived from realistic YN interaction models

and compared successfully with (π,K) data

Challenging physics :

Universal TBR

Pauli-forbidden states in ∑N